

from __future__ import annotations

from decimal import Decimal

from numpy import array



def   __UpperCAmelCase					(      __a :     list[list[float]]      )     ->	list[list[float]]:

					"""simple docstring"""

					_a      :       Optional[int]   =						Decimal

					# Check if the provided matrix has 2 rows and 2 columns
					# since this implementation only works for 2x2 matrices
					if len(__a      ) == 2 and len(matrix[0]      ) == 2 and len(matrix[1]      ) == 2:
										# Calculate the determinant of the matrix
										_a      :       Dict   =						float(
										    d(matrix[0][0]      ) * d(matrix[1][1]      ) - d(matrix[1][0]      ) * d(matrix[0][1]      )      )
										if determinant == 0:
															raise ValueError('''This matrix has no inverse.'''      )

										# Creates a copy of the matrix with swapped positions of the elements
										_a      :       str   =						[[0.0, 0.0], [0.0, 0.0]]
										_a ,   _a      :       int   =						matrix[1][1], matrix[0][0]
										_a ,   _a      :       Dict   =						-matrix[1][0], -matrix[0][1]

										# Calculate the inverse of the matrix
										return [
										    [(float(d(__a      )      ) / determinant) or 0.0 for n in row] for row in swapped_matrix
										]
					elif (
					    len(__a      ) == 3
					    and len(matrix[0]      ) == 3
					    and len(matrix[1]      ) == 3
					    and len(matrix[2]      ) == 3
					):
										# Calculate the determinant of the matrix using Sarrus rule
										_a      :       str   =						float(
										    (
										        (d(matrix[0][0]      ) * d(matrix[1][1]      ) * d(matrix[2][2]      ))
										        + (d(matrix[0][1]      ) * d(matrix[1][2]      ) * d(matrix[2][0]      ))
										        + (d(matrix[0][2]      ) * d(matrix[1][0]      ) * d(matrix[2][1]      ))
										    )
										    - (
										        (d(matrix[0][2]      ) * d(matrix[1][1]      ) * d(matrix[2][0]      ))
										        + (d(matrix[0][1]      ) * d(matrix[1][0]      ) * d(matrix[2][2]      ))
										        + (d(matrix[0][0]      ) * d(matrix[1][2]      ) * d(matrix[2][1]      ))
										    )      )
										if determinant == 0:
															raise ValueError('''This matrix has no inverse.'''      )

										# Creating cofactor matrix
										_a      :       Union[str, Any]   =						[
										    [d(0.0      ), d(0.0      ), d(0.0      )],
										    [d(0.0      ), d(0.0      ), d(0.0      )],
										    [d(0.0      ), d(0.0      ), d(0.0      )],
										]
										_a      :       Optional[Any]   =						(d(matrix[1][1]      ) * d(matrix[2][2]      )) - (
										    d(matrix[1][2]      ) * d(matrix[2][1]      )
										)
										_a      :       Dict   =						-(
										    (d(matrix[1][0]      ) * d(matrix[2][2]      )) - (d(matrix[1][2]      ) * d(matrix[2][0]      ))
										)
										_a      :       Tuple   =						(d(matrix[1][0]      ) * d(matrix[2][1]      )) - (
										    d(matrix[1][1]      ) * d(matrix[2][0]      )
										)
										_a      :       Tuple   =						-(
										    (d(matrix[0][1]      ) * d(matrix[2][2]      )) - (d(matrix[0][2]      ) * d(matrix[2][1]      ))
										)
										_a      :       Any   =						(d(matrix[0][0]      ) * d(matrix[2][2]      )) - (
										    d(matrix[0][2]      ) * d(matrix[2][0]      )
										)
										_a      :       Any   =						-(
										    (d(matrix[0][0]      ) * d(matrix[2][1]      )) - (d(matrix[0][1]      ) * d(matrix[2][0]      ))
										)
										_a      :       List[str]   =						(d(matrix[0][1]      ) * d(matrix[1][2]      )) - (
										    d(matrix[0][2]      ) * d(matrix[1][1]      )
										)
										_a      :       List[Any]   =						-(
										    (d(matrix[0][0]      ) * d(matrix[1][2]      )) - (d(matrix[0][2]      ) * d(matrix[1][0]      ))
										)
										_a      :       int   =						(d(matrix[0][0]      ) * d(matrix[1][1]      )) - (
										    d(matrix[0][1]      ) * d(matrix[1][0]      )
										)

										# Transpose the cofactor matrix (Adjoint matrix)
										_a      :       Union[str, Any]   =						array(__a      )
										for i in range(3      ):
															for j in range(3      ):
																				_a      :       Dict   =						cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
										_a      :       Optional[Any]   =						array(__a      )
										for i in range(3      ):
															for j in range(3      ):
																				inverse_matrix[i][j] /= d(__a      )

        # Calculate the inverse of the matrix
										return [[float(d(__a      )      ) or 0.0 for n in row] for row in inverse_matrix]
					raise ValueError('''Please provide a matrix of size 2x2 or 3x3.'''      )





import os
import sys
import tempfile

import torch

from .state import AcceleratorState
from .utils import PrecisionType, PrepareForLaunch, is_mps_available, patch_environment







def 							A__       (    lowerCamelCase  ,     lowerCamelCase=()  ,     lowerCamelCase=None  ,     lowerCamelCase="no"  ,     lowerCamelCase="29500"    )	->						List[Any]:
				UpperCamelCase_:				Any						=    False
				UpperCamelCase_:				int						=    False
				if any(key.startswith("""KAGGLE"""    ) for key in os.environ.keys()    ):
								UpperCamelCase_:				str						=    True
				elif "IPython" in sys.modules:
								UpperCamelCase_:				Tuple						=    """google.colab""" in str(sys.modules["""IPython"""].get_ipython()    )

				try:
								UpperCamelCase_:				Union[str, Any]						=    PrecisionType(mixed_precision.lower()    )
				except ValueError:
								raise ValueError(
								    F'''Unknown mixed_precision mode: {args.mixed_precision.lower()}. Choose between {PrecisionType.list()}.'''    )

				if (in_colab or in_kaggle) and (os.environ.get("""TPU_NAME"""  ,     lowerCamelCase    ) is not None):
								# TPU launch
								import torch_xla.distributed.xla_multiprocessing as xmp

								if len(AcceleratorState._shared_state    ) > 0:
												raise ValueError(
												    """To train on TPU in Colab or Kaggle Kernel, the `Accelerator` should only be initialized inside """
												    """your training function. Restart your notebook and make sure no cells initializes an """
												    """`Accelerator`."""    )
								if num_processes is None:
												UpperCamelCase_:				str						=    8

								UpperCamelCase_:				int						=    PrepareForLaunch(lowerCamelCase  ,     distributed_type="""TPU"""    )
								print(F'''Launching a training on {num_processes} TPU cores.'''    )
								xmp.spawn(lowerCamelCase  ,     args=lowerCamelCase  ,     nprocs=lowerCamelCase  ,     start_method="""fork"""    )
				elif in_colab:
								# No need for a distributed launch otherwise as it's either CPU or one GPU.
								if torch.cuda.is_available():
												print("""Launching training on one GPU."""    )
								else:
												print("""Launching training on one CPU."""    )
								function(*lowerCamelCase    )
				else:
								if num_processes is None:
												raise ValueError(
												    """You have to specify the number of GPUs you would like to use, add `num_processes=...` to your call."""    )

								if num_processes > 1:
												# Multi-GPU launch
												from torch.multiprocessing import start_processes
												from torch.multiprocessing.spawn import ProcessRaisedException

												if len(AcceleratorState._shared_state    ) > 0:
																raise ValueError(
																    """To launch a multi-GPU training from your notebook, the `Accelerator` should only be initialized """
																    """inside your training function. Restart your notebook and make sure no cells initializes an """
																    """`Accelerator`."""    )

												if torch.cuda.is_initialized():
																raise ValueError(
																    """To launch a multi-GPU training from your notebook, you need to avoid running any instruction """
																    """using `torch.cuda` in any cell. Restart your notebook and make sure no cells use any CUDA """
																    """function."""    )

												# torch.distributed will expect a few environment variable to be here. We set the ones common to each
												# process here (the other ones will be set be the launcher).
												with patch_environment(
												    world_size=lowerCamelCase  ,     master_addr="""127.0.01"""  ,     master_port=lowerCamelCase  ,     mixed_precision=lowerCamelCase    ):
																UpperCamelCase_:				Optional[int]						=    PrepareForLaunch(lowerCamelCase  ,     distributed_type="""MULTI_GPU"""    )
																print(F'''Launching training on {num_processes} GPUs.'''    )
																try:
																				start_processes(lowerCamelCase  ,     args=lowerCamelCase  ,     nprocs=lowerCamelCase  ,     start_method="""fork"""    )
																except ProcessRaisedException as e:
																				if "Cannot re-initialize CUDA in forked subprocess" in e.args[0]:
																								raise RuntimeError(
																								    """CUDA has been initialized before the `notebook_launcher` could create a forked subprocess. """
																								    """This likely stems from an outside import causing issues once the `notebook_launcher()` is called. """
																								    """Please review your imports and test them when running the `notebook_launcher()` to identify """
																								    """which one is problematic."""    ) from e

								else:
												# No need for a distributed launch otherwise as it's either CPU, GPU or MPS.
												if is_mps_available():
																UpperCamelCase_:				List[Any]						=    """1"""
																print("""Launching training on MPS."""    )
												elif torch.cuda.is_available():
																print("""Launching training on one GPU."""    )
												else:
																print("""Launching training on CPU."""    )
												function(*lowerCamelCase    )







def 							A__       (    lowerCamelCase  ,     lowerCamelCase=()  ,     lowerCamelCase=2    )	->						List[str]:
				from torch.multiprocessing import start_processes

				with tempfile.NamedTemporaryFile() as tmp_file:
								# torch.distributed will expect a few environment variable to be here. We set the ones common to each
								# process here (the other ones will be set be the launcher).
								with patch_environment(
								    world_size=lowerCamelCase  ,     master_addr="""127.0.01"""  ,     master_port="""29500"""  ,     accelerate_mixed_precision="""no"""  ,     accelerate_debug_rdv_file=tmp_file.name  ,     accelerate_use_cpu="""yes"""  ,     ):
												UpperCamelCase_:				str						=    PrepareForLaunch(lowerCamelCase  ,     debug=lowerCamelCase    )
												start_processes(lowerCamelCase  ,     args=lowerCamelCase  ,     nprocs=lowerCamelCase  ,     start_method="""fork"""    )






